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<a href="_variational_autoencoder_error_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment"> * </span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> *</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> * \brief       Variational-autoencoder error function</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> * </span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> * </span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> *</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> * \author      O.Krause</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> * \date        2017</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> *</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> *</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * </span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * </span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published </span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * </span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * </span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> *</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment"> */</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="preprocessor">#ifndef SHARK_OBJECTIVEFUNCTIONS_NEGATIVE_LOG_LIKELIHOOD_H</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="preprocessor">#define SHARK_OBJECTIVEFUNCTIONS_NEGATIVE_LOG_LIKELIHOOD_H</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span><span class="preprocessor">#include &lt;<a class="code" href="_abstract_model_8h.html">shark/Models/AbstractModel.h</a>&gt;</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="preprocessor">#include &lt;<a class="code" href="_abstract_objective_function_8h.html" title="AbstractObjectiveFunction.">shark/ObjectiveFunctions/AbstractObjectiveFunction.h</a>&gt;</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#include &lt;<a class="code" href="_random_8h.html">shark/Core/Random.h</a>&gt;</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a>{</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="comment"></span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="comment">/// \brief Computes the variational autoencoder error function</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="comment">///</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="comment">/// We want to optimize a model \f$ p(x) = \int p(x|z) p(z) dz \f$ where we choose p(z) as a multivariate normal distribution</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="comment">/// and p(x|z) is an arbitrary model, e.g. a deep neural entwork. The naive solution is sampling from p(z) and then compute the sample</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="comment">/// average. This will fail when p(z|x) is a very localized distribution and we might need many samples from p(z) to find a sample which is likely under</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="comment">/// p(z|x). p(z|x) is assumed to be intractable to compute, so we introduce a second model q(z|x), modeling p(z|x) and we want to train</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="comment">/// it such that it learns the unknown p(z|x). For this a variational lower bound on the likelihood is used and we maximize</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span><span class="comment">/// \f[  log p(x) \leq E_{q(z|x)}[\log p(x|z)] - KL[q(z|x) || p(z)] \f]</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="comment">/// The first term explains the meaning of variational autoencoder: we first sample z given x using the encoder model q and then decode</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span><span class="comment">/// z to obtain an estimate for x. The only difference to normal autoencoders is that we now have a probabilistic z. The second term ensures that</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="comment">/// q is learning p(z|x), assuming that we have enough modeling capacity to actually learn it. </span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span><span class="comment">/// See https://arxiv.org/abs/1606.05908 for more background.</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span><span class="comment">///</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span><span class="comment">/// Implementation notice: we assume q(z|x) to be a set of independent gaussian distributions parameterized as</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span><span class="comment">/// \f$ q(z| mu(x), \log \sigma^2(x)) \f$.</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span><span class="comment">/// The provided encoder model q must therefore have twice as many outputs as the decvoder has inputs as</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span><span class="comment">/// the second half of outputs is interpreted as the log of the variance. So if z should be a 100 dimensional variable, q must have 200</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span><span class="comment">/// outputs. The outputs and loss function used for the encoder p is arbitrary, but a SquaredLoss will work well, however also other losses </span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span><span class="comment">/// like pixel probabilities can be used.</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span><span class="comment">/// \ingroup objfunctions</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span><span class="comment"></span> </div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="keyword">template</span>&lt;<span class="keyword">class</span> SearchPo<span class="keywordtype">int</span>Type&gt;</div>
<div class="foldopen" id="foldopen00063" data-start="{" data-end="};">
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"><a class="line" href="classshark_1_1_variational_autoencoder_error.html">   63</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_variational_autoencoder_error.html" title="Computes the variational autoencoder error function.">VariationalAutoencoderError</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_abstract_objective_function.html" title="Super class of all objective functions for optimization and learning.">AbstractObjectiveFunction</a>&lt;SearchPointType, double&gt;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>{</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="keyword">typedef</span> <span class="keyword">typename</span> SearchPointType::device_type device_type;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keyword">typedef</span> <span class="keyword">typename</span> SearchPointType::value_type value_type;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="keyword">typedef</span> blas::matrix&lt;value_type, blas::row_major, device_type&gt; MatrixType;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"><a class="line" href="classshark_1_1_variational_autoencoder_error.html#a507e5d525e3ba1bf870a36c6c0b04a86">   70</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_unlabeled_data.html" title="Data set for unsupervised learning.">UnlabeledData&lt;SearchPointType&gt;</a> <a class="code hl_typedef" href="classshark_1_1_variational_autoencoder_error.html#a507e5d525e3ba1bf870a36c6c0b04a86">DatasetType</a>;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"><a class="line" href="classshark_1_1_variational_autoencoder_error.html#a1bcef582ede4db4936b7d6191949000d">   71</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_abstract_model.html" title="Base class for all Models.">AbstractModel&lt;SearchPointType,SearchPointType, SearchPointType&gt;</a> <a class="code hl_typedef" href="classshark_1_1_variational_autoencoder_error.html#a1bcef582ede4db4936b7d6191949000d">ModelType</a>;</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span> </div>
<div class="foldopen" id="foldopen00073" data-start="{" data-end="}">
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"><a class="line" href="classshark_1_1_variational_autoencoder_error.html#a60064ffe8b1119e6f63af647e7298e91">   73</a></span>    <a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#a60064ffe8b1119e6f63af647e7298e91">VariationalAutoencoderError</a>(</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        <a class="code hl_class" href="classshark_1_1_unlabeled_data.html">DatasetType</a> <span class="keyword">const</span>&amp; data,</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>        <a class="code hl_class" href="classshark_1_1_abstract_model.html" title="Base class for all Models.">ModelType</a>* encoder,</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <a class="code hl_class" href="classshark_1_1_abstract_model.html" title="Base class for all Models.">ModelType</a>* decoder,</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        <a class="code hl_class" href="classshark_1_1_abstract_loss.html" title="Loss function interface.">AbstractLoss&lt;SearchPointType, SearchPointType&gt;</a>* visible_loss,</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <span class="keywordtype">double</span> lambda = 1.0</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    ):mep_decoder(decoder), mep_encoder(encoder), mep_loss(visible_loss), m_data(data), m_lambda(lambda){</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        <span class="keywordflow">if</span>(mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_abstract_model.html#ae04810c1ae40f816872eba4ef3953e36" title="Returns true when the first parameter derivative is implemented.">hasFirstParameterDerivative</a>() &amp;&amp; mep_encoder-&gt;<a class="code hl_function" href="classshark_1_1_abstract_model.html#ae04810c1ae40f816872eba4ef3953e36" title="Returns true when the first parameter derivative is implemented.">hasFirstParameterDerivative</a>())</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            this-&gt;<a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#ad8888c58fd3f98e73013afb5dd4b2af1">m_features</a> |= this-&gt;<a class="code hl_enumvalue" href="classshark_1_1_abstract_objective_function.html#aadafeb6dfb5b649f321e7b81ac8aad1aa0bc7673a369df5f86ddd6ba6735f4971" title="The method evalDerivative is implemented for the first derivative and returns a sensible value.">HAS_FIRST_DERIVATIVE</a>;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        this-&gt;<a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#ad8888c58fd3f98e73013afb5dd4b2af1">m_features</a> |= this-&gt;<a class="code hl_enumvalue" href="classshark_1_1_abstract_objective_function.html#aadafeb6dfb5b649f321e7b81ac8aad1aab9262b57bb302f04b2561666a9068446" title="The function can propose a sensible starting point to search algorithms.">CAN_PROPOSE_STARTING_POINT</a>;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        this-&gt;<a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#ad8888c58fd3f98e73013afb5dd4b2af1">m_features</a> |= this-&gt;<a class="code hl_enumvalue" href="classshark_1_1_abstract_objective_function.html#aadafeb6dfb5b649f321e7b81ac8aad1aa9022946d8a121d3e6c820f58d8cd3d87" title="The function value is perturbed by some kind of noise.">IS_NOISY</a>;</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    }</div>
</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span><span class="comment"></span> </div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span><span class="comment">    /// \brief From INameable: return the class name.</span></div>
<div class="foldopen" id="foldopen00087" data-start="{" data-end="}">
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"><a class="line" href="classshark_1_1_variational_autoencoder_error.html#af6f7db424236e972169be485df11f212">   87</a></span><span class="comment"></span>    std::string <a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#af6f7db424236e972169be485df11f212" title="From INameable: return the class name.">name</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span><span class="keyword">    </span>{ <span class="keywordflow">return</span> <span class="stringliteral">&quot;VariationalAutoencoderError&quot;</span>; }</div>
</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span> </div>
<div class="foldopen" id="foldopen00090" data-start="{" data-end="}">
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"><a class="line" href="classshark_1_1_variational_autoencoder_error.html#a5e6dd6b42efb979395d221900550c7bb">   90</a></span>    <a class="code hl_typedef" href="classshark_1_1_abstract_objective_function.html#a59bfea031628e16737c66e7117eba7b5">SearchPointType</a> <a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#a5e6dd6b42efb979395d221900550c7bb" title="Proposes a starting point in the feasible search space of the function.">proposeStartingPoint</a>()<span class="keyword"> const</span>{</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        <span class="keywordflow">return</span> mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#afaa2ba692ab64a0edbff60d7ee6794db" title="Return the parameter vector.">parameterVector</a>() | mep_encoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#afaa2ba692ab64a0edbff60d7ee6794db" title="Return the parameter vector.">parameterVector</a>();</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    }</div>
</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    </div>
<div class="foldopen" id="foldopen00094" data-start="{" data-end="}">
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"><a class="line" href="classshark_1_1_variational_autoencoder_error.html#a2ab70e47d4d58df274f7092aac9aff67">   94</a></span>    std::size_t <a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#a2ab70e47d4d58df274f7092aac9aff67" title="Accesses the number of variables.">numberOfVariables</a>()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        <span class="keywordflow">return</span> mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#aed1e8d1d4dbde387e2f6a25141ed3a20" title="Return the number of parameters.">numberOfParameters</a>() + mep_encoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#aed1e8d1d4dbde387e2f6a25141ed3a20" title="Return the number of parameters.">numberOfParameters</a>();</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    }</div>
</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    </div>
<div class="foldopen" id="foldopen00098" data-start="{" data-end="}">
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"><a class="line" href="classshark_1_1_variational_autoencoder_error.html#ac5d3fa3f5711e3556e83d536e2e4bcb9">   98</a></span>    MatrixType <a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#ac5d3fa3f5711e3556e83d536e2e4bcb9">sampleZ</a>(<a class="code hl_typedef" href="classshark_1_1_abstract_objective_function.html#a59bfea031628e16737c66e7117eba7b5">SearchPointType</a> <span class="keyword">const</span>&amp; parameters, MatrixType <span class="keyword">const</span>&amp; batch)<span class="keyword"> const</span>{</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#ad5e35d1a10ff36fa72ea787baa40e9ad" title="Set the parameter vector.">setParameterVector</a>(subrange(parameters,0,mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#aed1e8d1d4dbde387e2f6a25141ed3a20" title="Return the number of parameters.">numberOfParameters</a>()));</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        mep_encoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#ad5e35d1a10ff36fa72ea787baa40e9ad" title="Set the parameter vector.">setParameterVector</a>(subrange(parameters,mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#aed1e8d1d4dbde387e2f6a25141ed3a20" title="Return the number of parameters.">numberOfParameters</a>(), <a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#a2ab70e47d4d58df274f7092aac9aff67" title="Accesses the number of variables.">numberOfVariables</a>()));</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>        </div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        MatrixType hiddenResponse = (*mep_encoder)(batch);</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        <span class="keyword">auto</span> <span class="keyword">const</span>&amp; mu = columns(hiddenResponse,0,hiddenResponse.size2()/2);</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        <span class="keyword">auto</span> <span class="keyword">const</span>&amp; log_var = columns(hiddenResponse,hiddenResponse.size2()/2, hiddenResponse.size2());</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        <span class="comment">//sample random point from distribution</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        MatrixType epsilon = blas::normal(*this-&gt;<a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#a6a27bddca6060f7861c49b05f8ec8435">mep_rng</a>,mu.size1(), mu.size2(), value_type(0.0), value_type(1.0), device_type());</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        <span class="keywordflow">return</span> mu + exp(0.5*log_var) * epsilon;</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    }</div>
</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span> </div>
<div class="foldopen" id="foldopen00110" data-start="{" data-end="}">
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"><a class="line" href="classshark_1_1_variational_autoencoder_error.html#a1c248c666ed60b7f985a5e05f2a822c8">  110</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#a1c248c666ed60b7f985a5e05f2a822c8" title="Evaluates the objective function for the supplied argument.">eval</a>(<a class="code hl_typedef" href="classshark_1_1_abstract_objective_function.html#a59bfea031628e16737c66e7117eba7b5">SearchPointType</a> <span class="keyword">const</span>&amp; parameters)<span class="keyword"> const</span>{</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(parameters.size() == <a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#a2ab70e47d4d58df274f7092aac9aff67" title="Accesses the number of variables.">numberOfVariables</a>());</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        this-&gt;<a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#af0942c072be06d0dd4da5ee7067c5777" title="Evaluation counter, default value: 0.">m_evaluationCounter</a>++;</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#ad5e35d1a10ff36fa72ea787baa40e9ad" title="Set the parameter vector.">setParameterVector</a>(subrange(parameters,0,mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#aed1e8d1d4dbde387e2f6a25141ed3a20" title="Return the number of parameters.">numberOfParameters</a>()));</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        mep_encoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#ad5e35d1a10ff36fa72ea787baa40e9ad" title="Set the parameter vector.">setParameterVector</a>(subrange(parameters,mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#aed1e8d1d4dbde387e2f6a25141ed3a20" title="Return the number of parameters.">numberOfParameters</a>(), <a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#a2ab70e47d4d58df274f7092aac9aff67" title="Accesses the number of variables.">numberOfVariables</a>()));</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        </div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        <span class="keyword">auto</span> <span class="keyword">const</span>&amp; batch = m_data.<a class="code hl_function" href="group__shark__globals.html#ga73034ee5639176b0d45e1059859d0f0a">batch</a>(<a class="code hl_function" href="namespaceshark_1_1random.html#aa64d4174eaf7111b03e0504eaa56b666" title="Draws a discrete number in {low,low+1,...,high} by drawing random numbers from rng.">random::discrete</a>(*this-&gt;<a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#a6a27bddca6060f7861c49b05f8ec8435">mep_rng</a>, std::size_t(0), m_data.<a class="code hl_function" href="group__shark__globals.html#gabd82edf467b9b82f4b0a1e70fd695311" title="Returns the number of batches of the set.">numberOfBatches</a>() -1));</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        MatrixType hiddenResponse = (*mep_encoder)(batch);</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        <span class="keyword">auto</span> <span class="keyword">const</span>&amp; mu = columns(hiddenResponse,0,hiddenResponse.size2()/2);</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        <span class="keyword">auto</span> <span class="keyword">const</span>&amp; log_var = columns(hiddenResponse,hiddenResponse.size2()/2, hiddenResponse.size2());</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        <span class="comment">//compute kulback leibler divergence term</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        <span class="keywordtype">double</span> klError = 0.5 * (sum(exp(log_var)) + sum(<a class="code hl_function" href="group__shark__globals.html#gae1f82613484173e9fe1a07960dabff63" title="Calculates x^2.">sqr</a>(mu))  - mu.size1() * mu.size2()  - sum(log_var));</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        <span class="comment">//sample random point from distribution</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        MatrixType epsilon = blas::normal(*this-&gt;<a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#a6a27bddca6060f7861c49b05f8ec8435">mep_rng</a>,mu.size1(), mu.size2(), value_type(0.0), value_type(1.0), device_type());</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        MatrixType z = mu + exp(0.5*log_var) * epsilon;</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>        <span class="comment">//reconstruct and compute reconstruction error</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        MatrixType reconstruction = (*mep_decoder)(z);</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        <span class="keywordflow">return</span> (m_lambda * (*mep_loss)(batch, reconstruction) + klError) / batch.size1();</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    }</div>
</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    </div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    </div>
<div class="foldopen" id="foldopen00131" data-start="{" data-end="}">
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"><a class="line" href="classshark_1_1_variational_autoencoder_error.html#a8b3b2f63448cb50dbcac630b10982341">  131</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#a8b3b2f63448cb50dbcac630b10982341">evalDerivative</a>( </div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        <a class="code hl_typedef" href="classshark_1_1_abstract_objective_function.html#a59bfea031628e16737c66e7117eba7b5">SearchPointType</a> <span class="keyword">const</span>&amp; parameters, </div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        <a class="code hl_typedef" href="classshark_1_1_abstract_objective_function.html#a59bfea031628e16737c66e7117eba7b5">SearchPointType</a> &amp; derivative </div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    )<span class="keyword"> const</span>{</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(parameters.size() == <a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#a2ab70e47d4d58df274f7092aac9aff67" title="Accesses the number of variables.">numberOfVariables</a>());</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        this-&gt;<a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#af0942c072be06d0dd4da5ee7067c5777" title="Evaluation counter, default value: 0.">m_evaluationCounter</a>++;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#ad5e35d1a10ff36fa72ea787baa40e9ad" title="Set the parameter vector.">setParameterVector</a>(subrange(parameters,0,mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#aed1e8d1d4dbde387e2f6a25141ed3a20" title="Return the number of parameters.">numberOfParameters</a>()));</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        mep_encoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#ad5e35d1a10ff36fa72ea787baa40e9ad" title="Set the parameter vector.">setParameterVector</a>(subrange(parameters,mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#aed1e8d1d4dbde387e2f6a25141ed3a20" title="Return the number of parameters.">numberOfParameters</a>(), <a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#a2ab70e47d4d58df274f7092aac9aff67" title="Accesses the number of variables.">numberOfVariables</a>()));</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        </div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        boost::shared_ptr&lt;State&gt; stateEncoder = mep_encoder-&gt;<a class="code hl_function" href="classshark_1_1_abstract_model.html#a47d80a74ce80e5dd5e2851c52738b86b" title="Creates an internal state of the model.">createState</a>();</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        boost::shared_ptr&lt;State&gt; stateDecoder = mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_abstract_model.html#a47d80a74ce80e5dd5e2851c52738b86b" title="Creates an internal state of the model.">createState</a>();</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        <span class="keyword">auto</span> <span class="keyword">const</span>&amp; batch = m_data.<a class="code hl_function" href="group__shark__globals.html#ga73034ee5639176b0d45e1059859d0f0a">batch</a>(<a class="code hl_function" href="namespaceshark_1_1random.html#aa64d4174eaf7111b03e0504eaa56b666" title="Draws a discrete number in {low,low+1,...,high} by drawing random numbers from rng.">random::discrete</a>(*this-&gt;<a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#a6a27bddca6060f7861c49b05f8ec8435">mep_rng</a>, std::size_t(0), m_data.<a class="code hl_function" href="group__shark__globals.html#gabd82edf467b9b82f4b0a1e70fd695311" title="Returns the number of batches of the set.">numberOfBatches</a>() -1));</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        MatrixType hiddenResponse;</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        mep_encoder-&gt;<a class="code hl_function" href="classshark_1_1_abstract_model.html#ac7edef74da55322b6aef0ba65b08592d" title="Standard interface for evaluating the response of the model to a batch of patterns.">eval</a>(batch,hiddenResponse,*stateEncoder);</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        <span class="keyword">auto</span> <span class="keyword">const</span>&amp; mu = columns(hiddenResponse,0,hiddenResponse.size2()/2);</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        <span class="keyword">auto</span> <span class="keyword">const</span>&amp; log_var = columns(hiddenResponse,hiddenResponse.size2()/2, hiddenResponse.size2());</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        <span class="comment">//compute kulback leibler divergence term</span></div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        <span class="keywordtype">double</span> klError = 0.5 * (sum(exp(log_var)) + sum(<a class="code hl_function" href="group__shark__globals.html#gae1f82613484173e9fe1a07960dabff63" title="Calculates x^2.">sqr</a>(mu))  - mu.size1() * mu.size2() - sum(log_var));</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        MatrixType klDerivative = mu | (0.5 * exp(log_var) - 0.5);</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        MatrixType epsilon = blas::normal(*this-&gt;<a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#a6a27bddca6060f7861c49b05f8ec8435">mep_rng</a>,mu.size1(), mu.size2(), value_type(0.0), value_type(1.0), device_type());</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        MatrixType z = mu + exp(0.5*log_var) * epsilon;</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        MatrixType reconstructions;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_abstract_model.html#ac7edef74da55322b6aef0ba65b08592d" title="Standard interface for evaluating the response of the model to a batch of patterns.">eval</a>(z,reconstructions, *stateDecoder);</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>        </div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>        </div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>        <span class="comment">//compute loss derivative</span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>        MatrixType lossDerivative;</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        <span class="keywordtype">double</span> recError = m_lambda * mep_loss-&gt;<a class="code hl_function" href="classshark_1_1_abstract_loss.html#a71706ed4c40d1635db1c372ecf5c8686" title="evaluate the loss and its derivative for a target and a prediction">evalDerivative</a>(batch,reconstructions,lossDerivative);</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        lossDerivative *= m_lambda;</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        <span class="comment">//backpropagate error from the reconstruction loss to the Decoder</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        <a class="code hl_typedef" href="classshark_1_1_abstract_objective_function.html#a59bfea031628e16737c66e7117eba7b5">SearchPointType</a> derivativeDecoder;</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        MatrixType backpropDecoder;</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        mep_decoder-&gt;<a class="code hl_function" href="classshark_1_1_abstract_model.html#adb4966b597013417b5e9957c84485c8c" title="calculates weighted input and parameter derivative at the same time">weightedDerivatives</a>(z,reconstructions, lossDerivative,*stateDecoder, derivativeDecoder, backpropDecoder);</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        </div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        <span class="comment">//compute coefficients of the backprop from mep_decoder and the KL-term</span></div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        MatrixType backprop=(backpropDecoder | (backpropDecoder * 0.5*(z - mu))) + klDerivative;</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        <a class="code hl_typedef" href="classshark_1_1_abstract_objective_function.html#a59bfea031628e16737c66e7117eba7b5">SearchPointType</a> derivativeEncoder;</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>        mep_encoder-&gt;<a class="code hl_function" href="classshark_1_1_abstract_model.html#ad699b6b1f813c5cc3b3ed45f254dbc1d" title="calculates the weighted sum of derivatives w.r.t the parameters.">weightedParameterDerivative</a>(batch,hiddenResponse, backprop,*stateEncoder, derivativeEncoder);</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    </div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        derivative.resize(<a class="code hl_function" href="classshark_1_1_variational_autoencoder_error.html#a2ab70e47d4d58df274f7092aac9aff67" title="Accesses the number of variables.">numberOfVariables</a>());</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        noalias(derivative) = derivativeDecoder|derivativeEncoder;</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>        derivative /= batch.size1();</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>        <span class="keywordflow">return</span> (recError + klError) / batch.size1();</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    }</div>
</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span> </div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>    <a class="code hl_typedef" href="classshark_1_1_variational_autoencoder_error.html#a1bcef582ede4db4936b7d6191949000d">ModelType</a>* mep_decoder;</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    <a class="code hl_typedef" href="classshark_1_1_variational_autoencoder_error.html#a1bcef582ede4db4936b7d6191949000d">ModelType</a>* mep_encoder;</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>    <a class="code hl_class" href="classshark_1_1_abstract_loss.html" title="Loss function interface.">AbstractLoss&lt;SearchPointType, SearchPointType&gt;</a>* mep_loss;</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>    <a class="code hl_class" href="classshark_1_1_unlabeled_data.html" title="Data set for unsupervised learning.">UnlabeledData&lt;SearchPointType&gt;</a> m_data;</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>    <span class="keywordtype">double</span> m_lambda;</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>};</div>
</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span> </div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>}</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span><span class="preprocessor">#endif</span></div>
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